Q. 14.4( 65 Votes )

In Δ PQR, ST is a

Answer :

Given,


Also, PST = PRQ


Need to prove that PQR is an isosceles triangle.


If a line divides any two sides of a triangles in the same ratio then the same line is parallel to the third side.


Since, ST || QR


PST = PQR …………eq(1)


(Corresponding angles)


Also given PST = PRQ ……………eq(2)


From eq(1) and eq(2) we get


PQR = PRQ


Since, sides opposite to equal angles are equal


PR = PQ


two sides of PQR is equal


PQR is an isosceles triangle


Hence proved.


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